Cyclic thermal loads and stresses in two critical components of fusion reactors, including fusion-fission hybrids, are modeled and calculated. The two critical components are the solid wall adjacent to the fusion plasma (“first wall”) and the fissile fuel elements in the high-power density region of the blanket. These two components exemplify two limiting cases of thermal loading: The first-wall loads are generated by predominantly shallow energy deposition that may be approximated with a flux across the surface and the fuel elements loads are generated by volumetric heating. Two approaches are used to solve the heat conduction equation and to calculate the resulting stresses in terms of system parameters. The first is expansion into Fourier series and determination of periodic solutions; the second is analysis and superposition of single-pulse responses weighted with appropriate time delay and decay factors. Approximate closed-form expression for temperature excursions and thermal stresses are derived; these expressions may be evaluated conveniently and rapidly for comparison of different systems. The results provide a quantitative basis for trade-off studies and comparative assessments of different fusion reactor systems.